We're baaack!After a two week recovery period, Problem of the Week returns...

The problem of the week is a regular instalment hereat the geometry forum. Each weekend a high-school levelgeometry problem will be posted (though levels may bedifferent in the summer), and the following weekend asummary of solutions will be posted.

Please do not post solutions to the problem of the week;instead mail you answer along with as detailed a description of your method as necessary/possibleto pow@forum.swarthmore.edu. Solutions should bereceived by midnight Friday so they can be combinedand posted over the weekend.

Problem of the Week 8/16 - 8/20 1993

You are given 27 rectangular solids of dimensions a,b,c. How can they bepacked to fit into a cube whose sides are a + b + c? (One should add thata, b, and c are not too different. If c/a and c/b were extremely large,for instance, it would be trivial to stack them like logs. A precisestatement would be something like (a+b+c)^3 - 27abc < abc.)

Again, DO NOT POST SOLUTIONS. Mail them to pow@forum.swarthmore.edu by Friday.